Question

Multiply the polynomial by the monomial?

5b(`b^5`-`1/10` `b^3`+`1/15` `b^2`-`1/25`b+1)

Answer 1

`=5b^6-1/2b^4+1/3b^3-1/5b^2+5b`

Explanation:

Multiplication distributes term by term, thus:
`5b(b^5-1/10b^3+1/15b^2-1/25b+1)`
`=5b\timesb^5-5b\times1/10b^3+5b\times1/15b^2-5b\times1/25b+5b\times1`

Simplifying gets you:
`=5b^6-1/2b^4+1/3b^3-1/5b^2+5b`